Icositetraquasitruncated prismatotetracontoctachoron

Icositetraquasitruncated prismatotetracontoctachoron
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Iquatpic
Coxeter diagram	x3x4x3x4/3*b ()
Elements
Cells	96 hexagonal prisms, 24 great rhombicuboctahedra, 24 quasitruncated cuboctahedra, 24 cuboctatruncated cuboctahedra
Faces	288+288 squares, 384+384 hexagons, 144 octagons, 144 octagrams
Edges	576+576+576+576
Vertices	1152
Vertex figure	Irregular tetrahedron, edge lengths √2 (2), √3 (2), √2+√2 (1), and √2–√2 (1)
Measures (edge length 1)
Circumradius
Hypervolume	60
Dichoral angles	Cotco–6–hip: 150°
	Quitco–4–hip:
	Cotco–8/3–quitco: 135°
	Girco–6–quitco: 120°
	Cotco–8–girco: 45°
	Girco–4–hip:
Number of external pieces	1800
Level of complexity	122
Related polytopes
Army	Semi-uniform Gippic, edge lengths (octagons), (remaining edges of half the ditrigons), 1 (remaining edges of other ditrigons)
Regiment	Iquatpic
Conjugate	Icositetraquasitruncated prismatotetracontoctachoron
Convex core	Icositetrachoron
Abstract & topological properties
Flag count	27648
Euler characteristic	312
Orientable	Yes
Properties
Symmetry	F4, order 1152
Convex	No
Nature	Tame

The icositetraquasitruncated prismatotetracontoctachoron, or iquatpic, is a nonconvex uniform polychoron that consists of 96 hexagonal prisms, 24 great rhombicuboctahedra, 24 quasitruncated cuboctahedra, and 24 cuboctatruncated cuboctahedra. 1 of each type of cell join at each vertex.

Vertex coordinates[edit | edit source]

The vertices of an icositetraquasitruncated prismatotetracontoctachoron of edge length 1 are given by all permutations of:

$\left(\pm {\frac {1+3{\sqrt {2}}}{2}},\,\pm {\frac {2{\sqrt {2}}-1}{2}},\,\pm {\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {1}{2}}\right),$
$\left(\pm {\frac {3{\sqrt {2}}}{2}},\,\pm {\sqrt {2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {{\sqrt {2}}-1}{2}}\right),$
$\left(\pm {\frac {3{\sqrt {2}}-1}{2}},\,\pm {\frac {1+2{\sqrt {2}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}}\right).$